Hundreds of companies worldwide form a shadow network capable of providing money and logistical support for continued attacks by Al Qaeda and other loosely connected militants, investigators and financial regulators in Europe and the United States say.

A United Nations report this month concluded that Al Qaeda remained a threat partly because it retained access to between $30 million and $300 million controlled by ostensibly legitimate businesses associated with the terror network. Many of these suspected front companies, it said, are in countries with few regulations and can pack up and disappear overnight.

''The real problem for the Americans is not freezing bank accounts,'' a Swiss banking regulator said in a recent interview in Zurich. ''The bigger challenge is stopping the unknown number of apparently legitimate businesses set up to move money around the globe to terrorists.''

Nearly a year after Al Qaeda's base of operations in Afghanistan was destroyed, efforts to disrupt the flow of money to its remaining operatives in other parts of the world have become one of the primary goals of the United States and its allies. So far, the results have been mixed.

One instance of the elusive nature of Qaeda front companies is Maram, set up in Istanbul as a travel agency and import-export business by three men described by American investigators as Qaeda associates.

The investigators said in recent interviews that they suspected that the company had provided money and other assistance to Qaeda operatives traveling between Europe and Afghanistan and might have been involved in efforts to obtain material for nuclear weapons.

But after one of its principals, Mamdouh Mahmud Salim, was arrested on a trip to Germany and extradited to New York on terrorism charges in 1998, the company cleaned out its offices overnight and disappeared.

Counterterrorism experts in Europe and the United States also said Islamic charities continued to disburse funds to militants. The United Nations says governments are having a particularly difficult time regulating and monitoring the millions of dollars paid out by the charities.

In the latest instance of a possible connection between charities and militants, the Dutch newspaper Eindhovens Dagblad reported last week that the security police were investigating financial links between a Saudi-financed mosque in the southern Dutch city of Eindhoven and members of the group from Hamburg, Germany, that was involved in the Sept. 11 attacks.

The United Nations report said the terror network was ''alive and well,'' with access to considerable money. Senior American officials disagreed, saying arrests in Europe, Southeast Asia and elsewhere and the freezing of $112 million in suspected terrorist money had weakened the organization.

Stopping the money flow is the best way to stop terrorism, said David Aufhauser, the general counsel at the Treasury Department and the chief of an interagency task force on terrorist financing.

''Much of the intelligence war is, in fact, suspect -- the product of treachery, deceit, custodial interrogation, bribery and encrypted talk,'' Mr. Aufhauser said at an international symposium on economic crime in Cambridge, England, last week. ''But audit trails do not lie. They are diaries of terror.''

Not every transaction leaves an audit trail, however, and some experts question whether the money can be stopped, given the myriad means of transferring cash around the world. Much of the terror network's wealth has been shifted beyond the reach of banks, according to the European intelligence authorities and bank regulators.

Valentin Roschacher, the attorney general of Switzerland, said the consensus of officials in all major European banking states was that Al Qaeda had protected most of its assets by shifting from cash to diamonds and gold before the Sept. 11 strikes in the United States.

''They are able to function, and we believe they still have enough money to possibly carry out other attacks,'' Mr. Roschacher told reporters recently in Washington.

Nikos Passos, a professor at Temple University and a consultant to the Treasury Department on illegal money transfers, said, ''The chief parallel aim should be to stop the terrorists, because the financing system cannot be completely controlled.''

The Turkish business linked to Al Qaeda offers a lesson in the difficulty of monitoring seemingly legitimate enterprises.

Mr. Salim, a Sudanese engineer and longtime associate of Osama bin Laden, set up the company in Istanbul in November 1996 at a time when Al Qaeda was expanding its financial reach from Afghanistan and Sudan into Europe. In the incorporation statement filed with the Turkish authorities, Mr. Salim said Maram would be involved in travel and in imports and exports.

American investigators and prosecutors said Mr. Salim, 44, had a history of moving money and shopping for weapons for Al Qaeda. In 1994, he was involved in an attempt to buy nuclear material and in later efforts to develop chemical weapons, according to testimony last year at the trial of other suspects in the 1998 bombings of the American Embassies in Kenya and Tanzania.

Mr. Salim is awaiting trial in New York on charges related to his suspected role in the embassy bombings.

A few months after Mr. Salim created Maram, records show that he transferred shares in the company to two other men identified by the American authorities as Qaeda members.

One was Wael Hamza Jalaidan, 44, a Saudi businessman described by the American authorities as a founding member of Al Qaeda. Earlier this month, the governments of the United States and Saudi Arabia jointly designated Mr. Jalaidan as a financial supporter of Al Qaeda, meaning his assets will be frozen.

Mr. Jalaidan is on the board of the Rabita Trust, a Pakistan-based charity accused by the United States of providing logistical and financial support to Al Qaeda.

Attempts to reach Mr. Jalaidan were unsuccessful. The Saudi press has reported that he issued a statement last year saying he cut all ties with Mr. bin Laden in 1992.

A senior American government official said that Mr. Jalaidan was in Saudi Arabia and that Saudi officials knew his location, though he was not believed to be in custody.

The other partner in Maram was Muhammad Bayazied, 42, a Sudanese also involved in setting up businesses for Mr. bin Laden, according to testimony at the New York trial. He also took part with Mr. Salim in the attempt to buy nuclear material and handled substantial amounts of cash, Jamal Ahmed al-Fadl, a former Qaeda member now cooperating with the government, testified.

A senior American official in the region said Mr. Bayazied once lived in the United States and was believed to be an expert in explosives and chemical weapons.

By the mid-1990's, Istanbul had become a frequent transit point for Qaeda operatives traveling between Afghanistan, Sudan and Europe, the American and European intelligence authorities say. The German police said one suspected Qaeda recruiter, Muhammad Heidar Zammar, passed through the Istanbul 40 times traveling between Europe and Afghanistan.

The senior American official in the region said that Maram was suspected of making travel arrangements for Qaeda operatives and that there were strong suspicions that Mr. Salim and Mr. Bayazied continued their efforts to buy components for nuclear weapons.

''We don't know what they were doing for sure,'' the official said. ''They were up to no good, but we don't have any details.''

The suspicions that they may have been trying to buy nuclear components were buttressed by a Turkish accountant, Yavuz Subasi, who handled Maram's books.

Mr. Subasi said that the company had no real business transactions, but that Mr. Salim had traveled extensively in Russia, Romania and Bulgaria, countries where the authorities say nuclear material is sometimes available on the black market.

Mr. Salim and Mr. Bayazied lived in Istanbul with their families on and off for at least two years, but they never attracted any notice from the Turkish authorities. Neighbors said the men kept to themselves, though they said there were many visitors to their apartments who appeared to be Arab.

In September 1998, Mr. Salim was arrested in Germany at the request of American prosecutors and extradited to the United States. Within days, Maram's tiny office in a huge anonymous office building in Istanbul was cleared out.

''I just came one morning and saw the office was empty,'' said Ahmet Evgin, who runs a small restaurant nearby. ''Nobody knows what happens.''

By the time the security police came around asking questions a few months ago, he and other former neighbors said, there were no traces of what might have been an important cog in the Qaeda financial machinery.